I finished the second sock yesterday and I'm happy to say that not only my idea works, the sock fits! I immediately started the second one, as there are a few things I want to change, like how the increases are done. I'm also hoping that once I wash the socks that awful ladder will go away.
As you can see on the second photo, I made some mistake when doing the heels and there are bumps there... I'll try to come up with something else for the short rows. For now, I'm just happy the idea does work in real life :D